Australian Curriculum Mathematics Alignment Document_V8.2 Year 9 Content Descriptors Elaborations Math-U-See links Number and Algebra Real numbers Solve problems involving direct proportion. Explore the relationship between graphs and equations corresponding to simple rate problems (ACMNA208) Apply index laws to numerical expressions with integer indices (ACMNA209) Honours pre-algebra lesson 30 developing reasoning and problem solving Honours algebra 1 lesson 1, 2, 3 developing reasoning and problem solving identifying direct proportion in real-life contexts Pre-algebra lesson 19, 20 Honours pre-algebra lesson 19, 20 simplifying and evaluating numerical expressions, using involving both positive and negative integer indices Algebra 2 lesson 18, 19, 28-3, 28-4, 29-2, 29-3 Honours algebra 2 lesson 2, 3, 4, 5, 16, 19 Pre-algebra lesson 5, 6, 7 Algebra 1 lesson 17, 18 Honours algebra 1 lesson 21, 22 26 Express numbers in scientific notation (ACMNA210) Money and financial mathematics Solve problems involving simple interest (ACMNA211) representing extremely large and small numbers in scientific notation, and numbers expressed in scientific notation as whole numbers or decimals understanding that financial decisions can be assisted by mathematical calculations Algebra 2 lesson 1 Algebra 1 lesson 31 Honours algebra 1 lesson 31, 33 Honours algebra 2 lesson 3, 4 Honours algebra 1 lesson 15, 16, 24, 25 Patterns and algebra Extend and apply the index laws to variables, using positive integer indices and the zero index (ACMNA212) Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate (ACMNA213) understanding that index laws apply to variables as well as numbers Algebra 1 lesson 17, 18, 25 Honours algebra 1 lesson 21 understanding that the distributive law can be applied to algebraic expressions as well as numbers understanding the relationship between expansion and factorisation and identifying algebraic factors in algebraic expressions Pre-algebra lesson 25 Honours pre-algebra 1 lesson 25 Algebra 1 lesson 16, 19, 20, 21, 22, 23, 24, 25
Honours algebra 1 lesson 23, 26 Algebra 2 lesson 2, 5-3, 15, 28-2, 28-1 Honours algebra 2 lesson 15, 23 Linear and non-linear relationships Find the distance between two points located on the Cartesian plane using a range of strategies, including graphing software (ACMNA214) Find the midpoint and gradient of a line segment (interval) on the Cartesian plane using a range of strategies, including graphing software (ACMNA294) Sketch linear graphs using the coordinates of two points and solve linear equations (ACMNA215) investigating graphical and algebraic techniques for finding distance between two points using Pythagoras' theorem to calculate distance between two points investigating graphical and algebraic techniques for finding midpoint and gradient recognising that the gradient of a line is the same as the gradient of any line segment on that line determining linear rules from suitable diagrams, tables of values and graphs and describing them using both words and algebra Algebra 2 lesson 22 Algebra 1 lesson 20, 22 Honours algebra 1 lesson 7 Algebra 1 lesson 6, 7, 8, 9, 10 Honours algebra 1 lesson 10, 11, 13, 18 Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations (ACMNA296) graphing parabolas, and circles connecting x-intercepts of a graph to a related equation Honours algebra 2 lesson 29 Algebra 1 lesson 26 Honours algebra 1 lesson 19, 20 Algebra 2 lesson 23-2, 23-3, 24, 26 Honours algebra 2 lesson 21, 22
Measurement and Geometry Using units of measurement Calculate areas of composite shapes (ACMMG216) understanding that partitioning composite shapes into rectangles and triangles is a strategy for solving problems involving area Honours geometry lesson 9, 13 Honours pre-algebra lesson 15 Calculate the surface area and volume of cylinders and solve related problems (ACMMG217) Solve problems involving the surface area and volume of right prisms (ACMMG218) analysing nets of cylinders to establish formulas for surface area connecting the volume and capacity of a cylinder to solve authentic problems solving practical problems involving surface area and volume of right prisms Honours algebra 2 lesson 18 Geometry lesson 14, 16 Honours geometry lesson 14, 16 Pre-algebra lesson 24 Geometry lesson 15, 16 Honours geometry lesson 15, 16, 19 Pre-algebra lesson 15, 27 Investigate very small and very large time scales and intervals (ACMMG219) Geometric reasoning Use the enlargement transformation to explain similarity and develop the conditions for triangles to be similar (ACMMG220) Solve problems using ratio and scale factors in similar figures (ACMMG221) investigating the usefulness of scientific notation in representing very large and very small numbers Honours algebra 2 lesson 18 Algebra 1 lesson 31 Honours algebra 1 lesson 31, 33 Geometry lessons 1 and 2 are good for review and setting the scene for develop geometric reasoning. Honours geometry lesson 1, 11, 22 support the development of logical thinking and reasoning establishing the conditions for similarity of two triangles and comparing Geometry lesson 27 this to the conditions for congruence using the properties of similarity and ratio, and correct mathematical notation and language, to solve problems involving enlargement (for example, scale diagrams) using the enlargement transformation to establish similarity, understanding that similarity and congruence help describe relationships between geometrical shapes and are important elements of reasoning and proof establishing the relationship between areas of similar figures and the ratio Geometry lesson 27 of corresponding sides (scale factor) Honours geometry lesson 10, 20 Honours algebra 2 lesson 5, 6 Pythagoras and trigonometry Investigate Pythagoras Theorem and its application to solving simple problems involving right angled triangles (ACMMG222) understanding that Pythagoras' Theorem is a useful tool in determining unknown lengths in right-angled triangles and has widespread applications Geometry lesson 18, 20, 21 Honours geometry lesson 18, 21
recognising that right-angled triangle calculations may generate results that can be integers, fractions or irrational numbers Pre-algebra 1 lesson 11 Honours pre-algebra lesson 10, 13 Use similarity to investigate the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles (ACMMG223) Apply trigonometry to solve right-angled triangle problems (ACMMG224) developing understanding of the relationship between the corresponding sides of similar right-angled triangles understanding the terms 'adjacent' and 'opposite' sides in a right-angled triangle selecting and accurately using the correct trigonometric ratio to find unknown sides (adjacent, opposite and hypotenuse) and angles in rightangled triangles 1-1 Geometry lesson 26, 27 Honours geometry lesson 29 Geometry lesson 29 Honours geometry lesson 30 1-4, 31-5
Statistics and Probability Chance List all outcomes for two-step chance experiments, both with and without replacement using tree diagrams or arrays. Assign probabilities to outcomes and determine probabilities for events (ACMSP225) Calculate relative frequencies from given or collected data to estimate probabilities of events involving 'and' or 'or' (ACMSP226) Investigate reports of surveys in digital media and elsewhere for information on how data were obtained to estimate population means and medians (ACMSP227) Data representation and interpretation Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly and from secondary sources (ACMSP228) Construct back-to-back stem-and-leaf plots and histograms and describe data, using terms including skewed, symmetric and bi modal (ACMSP282) Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread (ACMSP283) conducting two-step chance experiments using systematic methods to list outcomes of experiments and to list outcomes favourable to an event comparing experiments which differ only by being undertaken with replacement or without replacement using Venn diagrams or two-way tables to calculate relative frequencies of events involving and, or questions using relative frequencies to find an estimate of probabilities of and, or events investigating a range of data and its sources, for example the age of residents in Australia, Cambodia and Tonga; the number of subjects studied at school in a year by 14-year-old students in Australia, Japan and Timor-Leste comparing the annual rainfall in various parts of Australia, Pakistan, New Guinea and Malaysia using stem-and-leaf plots to compare two like sets of data such as the heights of girls and the heights of boys in a class describing the shape of the distribution of data using terms such as positive skew, negative skew and 'symmetric' and 'bi-modal' comparing means, medians and ranges of two sets of numerical data which have been displayed using histograms, dot plots, or stem and leaf plots Geometry lesson 2 (set terminology) Honours pre-algebra lesson 27